Cluster calculations of ZnO with Cu and Ni impurities

The variational cellular method, extended to study crystalline structures, has been applied to 17-atom clusters representing a ZnO crystal without and with substitutional impurities. Self-consistent-field electronic-structure calculations were carried out for the substitutional Cu and Ni. The (2+)-charge ion states were studied and the optical transitions discussed in terms of Koopmans's theorem or transition-state calculations, depending on their range of applicability. The analysis of the results is preceded by a discussion on the general questions of to what extent a cluster can be used to calculate crystal energy bands and localized states.